if you can see a mive which treatens checkmate, should it always be played

Not necessarily. It is important to access other options as well. While threatening checkmate is often good, this simple example illustrates why that is not always the case. 3.Qf3 threatens checkmate but it can easily be blocked and now black has a lead in development.

There are few absolute rules when it comes to move selection in chess; it usually depends on a number of factors.

In this case two key factors would be whether threatening checkmate harms your position, and the time control.

To be honest, if you're playing blitz or faster time control, it's usually worth it to threaten mate -- they might miss it, and lose on the spot, and if not, it's unlikely they'll be a move that both defends the mate and puts you in trouble at the same time.

I guess a third factor might be if there is a better way to set up the threat. Like, if you line up a battery now, the opponent will likely see it and defend. But what if you have a knight also hovering nearby with threats of his own? And the battery appears via a discovery? In longer time control games it is probably worth considering additional factors like these.

More to the point, 4.Qxf6 threatens checkmate, but it's extremely stupid.

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No.

But in tactical situations it's useful to challenge yourself to find all the ways to threaten mate in 1 (also during any point in the middle of a calculation). Because even though most of them will be stupid sacrifices, sometimes those moves lead to a winning tactic, or form the basis for a winning tactic.

Another example.